Form and Structure of African Music: A Generative Theory of Structural Organization by Willie Anku

Abstract

This book is the product of many years of work by Willie Anku who has used mathematical set theory to analyse the multi-rhythmic structures of African drum-dances. In it he examines eight pieces of Ghanaian music to explore a completely new way of de-composing African music, as the building blocks of set theory, as applied to rhythm, are groupings of percussive notes rather than the individual ones found in standard western systems. For instance, music-scores use a divisive note system (from large to increasingly smaller time values) as well as bar lines and accents that are all difficult and cumbersome to apply to poly-rhythmic music. Likewise, the graphical Time Unit Box (TUB) System developed in the United States, although useful, is a graphical system based on a ‗density referent‘ or lowest rhythmic common denominator. This super fine quantification of time is not actually employed by African musicians who, for instance, convey percussive information through mnemonic phrases that represent patterned groups of notes. The principal set in Anku‘s system are the percussive notes or ‗attack points‘ that comprise one ‗time-line‘ of the bell pattern that is repeated in ostinato fashion. Then there are sub-sets based on small rhythmic patterns within the main-set. At a higher hierarchical level there are super-sets that span several sets and are played out in the lengthy passages of master drummers. Although the set is the basic structural unit of Anku‘s system, it is the small quarter and half set rhythms that are the basic units of this system, and not the single notes and graphical lines of western scores and the TUB System. One such subset is a simple half-set: a forward propelling ‗call‘ followed in ‗response‘ by a resolving half. The renowned musicologist Prof. J. H. K. Nketia has also noted this polarised tension-release feature of African time-lines. Then there is the division of the set into four regulative ‗beat areas‘ that will be discussed later. I should add here that in the classroom Anku used some of the short half and quarter set patterns to teach rhythmic skills to his students by showing them notated on a pack of that he called ‗flash cards,‘ which the students had to recognise and play in a gestalt ‗flash.‘ This gestalt way of teaching is closer to the African way of conceiving music as patterns rather than as sequences of individual notes. It is also the holistic awareness of these quarters and half set rhythms that allow African master musicians to easily use them to make short rhythmic bridges and interpolations that are repeated to make a complete set, or added to incomplete sets until they resolve within the isometric bell pattern of the main set. The main set, as mentioned, is equivalent to one span of the time-line. In the various types of music Anku analyses these are in duple time (2/4), triple time (6/8) and thirdly compound 117 polyrhythmic time that exhibits both duple and triple properties. For each of these three classes of rhythm Anku has created a standard ‗ideal type‘ template, from which the various bell patterns of the drum-dances he examines can be fitted. This system can of course be applied to other Ghanaian and indeed continental African drum-dances based on duple, triple and compound time: that can all be treated as variations of the particular standard or template set form. A common feature of all the eight drum dances that Anku analysed is that there are four regularly spaced ‗felt pulses‘ that are implicit in all the rhythmic sets and divide them into the four ‗beat areas‘ mentioned previously. These felt pulses are not necessarily played by any drum or percussion instrument but help anchor the music (and dance-steps). These un-played grouping of regular pulses is somewhat akin to what the pioneering American ethnomusicologist Richard Waterman called the ‗subjective metronome sense‘ found in Black American music. Within the circular main-set itself one of these four ‗felt pulses‘ acts as a ‗Regulative Time Point‘ (RTP) which fall on a critical juncture where several rhythmic beginnings or endings coincide. However, it does not necessarily have to coincide with the beginning of the circular set‘s time-line: i.e. the first beat of the bell. These RTP‘s are in fact culture bound – which explains why, although the Ghanaian Ewe agbadza and Nigerian Yoruba kon-kon bell patterns are structurally identical, their beginnings, in terms of their RTP‘s, are located at different points on the set circle. It is because the RTP does not necessarily have to coincide with what a particular African society considers the first beat of the bell that musicologists, like Kofi Agawu and John Chernoff, talk of ‗unarticulated‘ or ‗hidden‘ beats in African music. The occasional non-correspondence between the RTP and first beat of the bell also explains the problems that many non-African have in determining where a piece of African music begins Willie Anku diagrammatically depicts the main set, that is the ostinato bell pattern, as a circle. This firstly allows one to see the set holistically, with its beginning and end adjacent. Secondly, this circular depiction allows one to easily compare the bell pattern (and other simple one set rhythms) of different African societies as simple rotations of one another on a circle: i.e. the same rhythmic structure but with different starting points. Thirdly, it clearly portrays the various pulses of the bell pattern that act as entrance points for the various staggered support and master rhythms that constitute the musical piece. On paper Anku depicts these staggered poly-rhythms as circles branching out from the main set circle of the bell time-line and interlocking with it at their particular starting points. Finally, there is the super-set which involves complex master drum patterns that span multiple sets. Anku makes the interesting point that the repetitive bell and other support rhythms that fall within the main set can be treated as a the steady drone, over which the master drummers (and indeed dancers) extemporise. On paper Anku displays these extended master drum phrases as a chain of adjacent or interlocking circles emanating and branching off from the main circular set, creating a constellation of interlocking circles surrounding and ultimately traceable to the main set. This represents the spiralling movement of the master drum patterns in time, impossible to draw on paper. Willie Anku has therefore devised a two-dimensional way of representing the various super-sets as they branch off from the main one. He calls this two-dimensional composite a ‗performance map.